Structure of the Liquidâ Vapor Interface of Waterâ Methanol Mixtures

J. Phys. Chem. B 2005, 109, 20493-20503

20493

Structure of the Liquid-Vapor Interface of Water-Methanol Mixtures as Seen from Monte Carlo Simulations Lı´via Pa´ rtay and Pa´ l Jedlovszky* Department of Colloid Chemistry, Eo¨tVo¨s Lora´ nd UniVersity, Pa´ zma´ ny Pe´ ter stny. 1/a, H-1117 Budapest, Hungary

A Ä rpa´ d Vincze Department of NBC and EnVironmental Security, Zrıńyi Miklo´ s National Defense UniVersity, Hunga´ ria krt. 9-11, H-1581 Budapest, Hungary

George Horvai Department of Chemical Information Technology, Budapest UniVersity of Technology and Economics, Gelle´ rt te´ r 4, H-1111 Budapest, Hungary ReceiVed: June 27, 2005; In Final Form: August 31, 2005

Monte Carlo simulation of the vapor-liquid interface of water-methanol mixtures of different compositions, ranging from pure water to pure methanol, have been performed on the canonical (N, V, T) ensemble at 298 K. The analysis of the systems simulated has revealed that the interface is characterized by a double layer structure: methanol is strongly adsorbed at the vapor side of the interface, whereas this adsorption layer is followed at its liquid side by a depletion layer of methanol of lower concentration than in the bulk liquid phase of the system. The dominant feature of the interface has been found to be the adsorption layer in systems of methanol mole fractions below 0.2, and the depletion layer in systems of methanol mole fractions between 0.25 and 0.5. The orientation of the molecules located at the depletion layer is found to be already uncorrelated with the interface, whereas the methanol molecules of the adsorption layer prefer to align perpendicular to the interface, pointing straight toward the vapor phase by their methyl group. Although both the preference of the molecular plane for a perpendicular alignment with the interface and the preference of the methyl group for pointing straight to the vapor phase are found to be rather weak, the preference of the methyl group for pointing as straight toward the vapor phase as possible within the constraint imposed by the orientation of the molecular plane is found to be fairly strong. One of the two preferred orientations of the interfacial water molecules present in the neat system is found to disappear in the presence of methanol, because methanol molecules aligned in their preferred orientation can replace these water molecules in the hydrogen-bonding pattern of the interface.

1. Introduction The atomistic-level structure of liquid-vapor interfaces has become the target of intensive scientific investigations in the past decade. This increasing scientific attention has been initiated by the rapid development of various surface-sensitive experimental methods, such as nonlinear (e.g., second harmonic generation or sum frequency generation) spectroscopies, X-ray and neutron reflection, and so forth. Experimental studies have successfully been complemented by investigations using computer simulation methods. Thus, the liquid-vapor interfaces of various neat systems1-22 and aqueous solutions2,23-32 have been investigated in detail both by experimental1-3,5,8-11,13-15,18,22,24,29,31,32 and by computer simulation methods4,6,7,11,12,16,17,19-21,23,25-28,30 in the past few years. Water-methanol mixtures of various compositions are among the most widely studied systems both in the bulk liquid phase33-42 and at the liquid-vapor interface.2,23-25,29,30,32 The scientific importance of these systems stems from the fact that methanol is the smallest possible hydrogen-bonding solute that also contains a hydrophobic (methyl) group, and hence, it shows, * E-mail: [email protected].

although in a considerably weaker form, all the important properties of the amphiphilic surfactant molecules from surface adsorption23,30,32 to aggregation in the bulk phase.41,42 The structure of the liquid-vapor interface of watermethanol mixtures has already been analyzed in detail on the basis of a set of molecular dynamics simulations in the pioneering work of Matsumoto et al.23 They have found that, although the methanol molecules are rather strongly adsorbed right at the interface, this interfacial layer is followed by a subsurface depletion layer at its liquid side, in which the methanol density is even smaller than in the bulk liquid phase. No such depletion layer has, however, been found in the recent simulation study of Chang and Dang using polarizable potential models for both water and methanol.30 It should be noted, however, that the performance of several simple, nonpolarizable water models, such as TIP4P43 or SPC/E44 in low-density states is, in many respects, superior to that of polarizable water models.45 Although the surface adsorption of methanol in water is a well-known experimental fact,46,47 the existence of the methanol-poor second layer has only been detected experimentally by Chen et al.32 using the polarization null angle (PNA) variant of the vibrational sum frequency generation (SFG)

10.1021/jp0534885 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/07/2005

20494 J. Phys. Chem. B, Vol. 109, No. 43, 2005 spectroscopy. In the PNA method, the orientation of a bond or a group is determined from the null angle of the corresponding peak of the visible SFG spectrum rather than from the intensity ratio of this peak as measured with different polarization combinations, which allows a considerably more accurate determination of the orientation of the interfacial methyl groups than the traditional way of interpreting the spectra.15,18,48,49 In their study, Chen et al. have concluded that the hydration free energy of the methanol molecules is about 7.1 ( 0.4 kJ/mol lower in the first (adsorption) and 2.1 ( 1.7 kJ/mol higher in the second (depletion) layer than in the bulk liquid phase.32 The orientation of the methanol molecules adsorbed at the interface has also been the subject of intensive investigations. Matsumoto et al. have found that the ordering of the interfacial methanol molecules is strong, and it is enhanced at lower methanol concentrations; however, the orientational preferences of the methanol molecules have not been specified.23 In a subsequent simulation study, Chang and Dang have concluded that in their preferred orientation interfacial methanol molecules point straight to the vapor phase by their methyl group, and this preference becomes weaker (i.e., the orientational distribution becomes broader) with increasing methanol concentrations.30 These findings are in accordance with the conclusions of several former experimental SFG studies, on the basis of the observation that the intensity of the sign drops with increasing methanol concentration.1-3,24,29,32 Thus, using the intensity ratio method, Wolfrum et al. have found that the average tilt angle of the methyl group relative to the interface normal axis is below 40° in pure methanol, and this angle is 0° in dilute aqueous methanol solutions, whereas the full widths of the corresponding orientational distributions at half-maximum have been found to be about 70° and 16°, respectively.2 Similar results have been obtained by Huang and Wu for the water-methanol mixture containing 5% methanol.24 Ma and Allen have also concluded that the interfacial methanol molecules become less ordered with increasing bulk methanol mole fractions above 0.57.29 However, these conclusions have been contradicted by Lu et al.15 and Chen et al.,32 who have directly measured the orientational parameter characterizing the alignment of the interfacial methyl groups using the PNA method in their SFG measurements, as they have found the interfacial methanol molecules to be considerably more ordered than in the previous studies. Thus, the average tilt angle of the methyl group has been found to be 0° ( 6° with a very narrow orientational distribution at the liquid-vapor interface of pure methanol.15 Furthermore, in a clear contrast with the previous studies,2,23,29,30 Chen et al. have found that the orientational order of the interfacial methanol molecules increases rather than decreases with increasing bulk methanol concentrations.32 Recently, we have demonstrated, on the example of the interfacial orientation of water50,51 and acetone,52 that the preferential orientation of entire molecules relative to an interface can only be described unambiguously by the bivariate distribution of two independent orientational parameters (e.g., the angular polar coordinates of the interface normal vector in a molecule-fixed local Cartesian coordinate frame50,51); the information obtained on the preferential orientation of various different molecule-fixed vectors cannot be simply put together without the risk of getting incorrect results. In this paper, we report a set of Monte Carlo simulations of the liquid-vapor interface of water-methanol mixtures of different compositions, also including pure water and pure methanol as reference systems. The resulting configurations are analyzed in terms of the orientational ordering of the molecules.

Pa´rtay et al. Particular attention is paid to the question of the existence of a depletion layer of methanol beside the adsorption layer right at the interface and to the determination of the full orientational statistics and orientational preferences of the interfacial molecules in different layers of the interface using bivariate distributions of two independent orientational parameters. The question of how the presence of the methanol molecules influences the orientation of the interfacial waters is also addressed. Since the completion of this work has mainly been motivated by the recent experimental study of Chen et al.,32 using the novel PNA method in SFG spectroscopy, which is claimed to be considerably more accurate than the traditional way of interpreting SFG spectra,15,18,48,49 our results are compared with the data of Chen et al.32 wherever possible. 2. Monte Carlo Simulations Monte Carlo simulation of the vapor-liquid interface of water-methanol mixtures of 10 different compositions have been performed on the canonical (N, V, T) ensemble at 298 K. The systems have consisted of 1000 molecules, among which 0, 50, 100, 150, 200, 250, 300, 500, 900, and 1000, respectively, have been methanols. These systems are referred to throughout this paper as the 0%, 5%, 10%, 15%, 20%, 25%, 30%, 50%, 90%, and 100% methanol systems, respectively. The length of the X edge of the rectangular basic simulation box, which has been perpendicular to the interface, has been 200 Å, whereas the Y and Z edges have been 25 Å long. Standard periodic boundary conditions have been applied. The water and methanol molecules have been described by the TIP4P potential43 and the model of van Leeuwen and Smit,53 respectively. Both models are rigid; the CH3 group of the methanol molecule is treated as a united atom. In choosing these rigid, nonpolarizable models for describing the water and methanol molecules, we have considered our earlier finding that, despite the indubitable importance of the nonadditive forces in describing the properties of systems showing large density variations, simple nonpolarizable water models originally designed to reproduce bulk liquidphase properties only, such as TIP4P43 or SPC/E,44 proved to be considerably more successful in describing several (e.g., thermodynamic, dielectric) properties of water in low-density states than the more sophisticated and computationally far more demanding polarizable water potentials.45 The interaction of two molecules has been truncated to zero at the center-center distance of 12.5 Å. The simulations have been performed using the program MMC.54 In every Monte Carlo step, a randomly chosen molecule has randomly been translated by no more than 0.25 Å and randomly rotated around a randomly chosen spacefixed axis by no more than 15°. On average, about one-third of the trial moves have been accepted. Initial configurations have been prepared by placing the molecules to a rectangular simulation box of the size of 46.7 Å × 25 Å × 25 Å and briefly equilibrating them by performing 106 Monte Carlo moves. Then, the liquid-vapor interfaces have been created by increasing the X edge of the basic box to 200 Å. The interfacial systems have been further equilibrated by performing another 5 × 108 Monte Carlo moves. To see whether equilibrium is reached, the energy as well as the density profile of the molecules has been calculated in blocks of 5 × 106 Monte Carlo moves. In the production phase, 2500 sample configurations per system, separated by 106 Monte Carlo steps each, have been saved for further analyses. Finally, the saved sample configurations have been translated along the interface normal axis X in such a way that the center-of-mass of the system has been placed to the position of X ) 0 Å, i.e., in the

Structure of Liquid-Vapor Interface of Water-MeOH Mixtures

J. Phys. Chem. B, Vol. 109, No. 43, 2005 20495 50% methanol content, its thickness slightly decreases with further increase of the methanol concentration. The methanol molecular number density profiles exhibit a clear peak at the interfacial region, indicating the surface adsorption of the methanol molecules. The difference between the height of this peak and the bulk liquid-phase value of Fm is larger at smaller methanol concentrations. It is also evident that on the liquid side of this adsorption peak the methanol density profiles go through a rather broad minimum, whereas the corresponding water profiles show a clear maximum at the same X values. This finding indicates, in a clear accordance both with the simulation results of Matsumoto et al.23 as well as with several simulations of the liquid-vapor interface of waterethanol mixtures,26,27 and also with the results of the recent SFG measurement of Chen et al.,32 the presence of a subsurface layer of low methanol concentration. The appearance of this depletion layer of methanol is the most evident at intermediate methanol concentrations. The excess hydration free energy of the methanol molecules at the adsorption and depletion layers relative to the bulk phase (∆Aa and ∆Ad, respectively) can be determined by converting the Fm(X) methanol number density profiles to methanol hydration free-energy profiles Am(X) as

Figure 1. Number density profile of the water (top) and methanol (middle) molecules and mass density profile (bottom) in eight different systems simulated. Solid curves, 0%; dotted lines, 5%; dash, 10%; dash-dot-dot, 20%; full circles, 30%; asterisks, 50%; open circles, 90%; short dash, 100% methanol system. The inset shows the division of the interfacial and subsurface regions of the systems to three separate layers, on the example of the 50% methanol system. All profiles shown are averaged over the two interfaces present in the basic simulation box.

TABLE 1: Calculated Properties of the Systems Simulated methanol mole fraction overall system

layer A

layer B

layer C

bulk phase

d10-90 (Å)

∆Aa (kJ/mol)

∆Ad (kJ/mol)

0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.500 0.900 1.000

0.000 0.406 0.582 0.649 0.706 0.733 0.727 0.743 0.949 1.000

0.000 0.101 0.181 0.262 0.312 0.334 0.338 0.545 0.890 1.000

0.000 0.030 0.068 0.124 0.169 0.199 0.229 0.445 0.871 1.000

0.000 0.029 0.085 0.128 0.172 0.240 0.339 0.524 0.906 1.000

3.5 4.3 4.4 4.6 4.6 4.7 4.9 6.9 6.5 5.4

-8.85 -9.25 -8.74 -8.74 -5.63 -0.76 0.00 -0.29 0.0

0.26 1.51 1.27 1.08 3.24 5.03 2.52 1.00 0.0

middle of the simulation box, to avoid the artificial broadening of the interface due to its translation along the X axis. 3. Results and Discussion 3.1. Density Profiles. The molecular number density profiles of the water and methanol molecules (Fw and Fm, respectively) as well as the mass density profile Fmass of the systems simulated along the interface normal axis X are shown in Figure 1. All profiles shown are averaged over the two interfaces present in the simulation box. The obtained mass density profiles show a sharp transition between the two phases: the 10-90 thickness of the interfaces d10-90 (i.e., the width of the X range within which the mass density of the system drops from 90% to 10% of its bulk liquid value) resulted between 3.5 and 7 Å in all eight systems simulated. The obtained d10-90 values, summarized in Table 1, show in accordance with the results of previous studies23,30 the general trend that the interfacial region becomes wider with increasing methanol mole fractions, although above

Am(X) ) -RT ln Fm(X) + C,

(1)

where R is the gas constant, T is the absolute temperature of the system, and C is an arbitrary constant up to which the Am(X) profile is determined by Fm(X). The obtained data listed in Table 1 agree well with the values of -7.1 ( 0.4 kJ/mol and 2.1 ( 1.7 kJ/mol, estimated by Chen et al. from their SFG measurements, using a double layer adsorption model and Langmuir isotherm for the excess hydration free energy of methanol in the adsorption and depletion layers, respectively.32 In comparing the obtained excess hydration free energy values with the experimental data, it has to be noted that Chen et al. have determined these values from the change of the effective interfacial density of the methyl groups with the methanol mole fraction, and hence, they had to assume that the values of both ∆Aa and ∆Ad do not change with the composition of the system,32 whereas here we could estimate the composition dependence of ∆Aa and ∆Ad. The obtained results indicate that such an assumption is only valid at low enough methanol concentrations (i.e., below 20%) for ∆Aa, as its value is found to be nearly constant in the methanol mole fraction range 0-0.2. However, above this concentration, the magnitude of ∆Aa decreases rapidly and drops nearly to zero above 30% methanol content in the system. On the other hand, the value of ∆Ad is considerably higher at intermediate methanol concentrations (i.e., between 25% and 50%) than in systems below or above this concentration range. These findings indicate that, while in systems containing less than 20% methanol the structure of the interface is dominated by the adsorption of the methanol molecules at the interface, in systems of methanol mole fraction of 0.25-0.5 the dominant feature of the interfacial structure is the presence of a subsurface depletion layer. For the purpose of the subsequent analyses, we have divided the interfacial and subsurface regions of the systems studied to three separate layers according to the behavior of the mass density profiles of the systems. Thus, layer A, located at the vapor side of the interface, extends from the X value at which the density of the system becomes different from zero up to where it reaches 50% of the bulk liquid value, whereas layers B and C are defined to be as wide as layer A. The division of the interface to three separate layers is illustrated at the inset of Figure 1, on the example of the 50% methanol system. The

20496 J. Phys. Chem. B, Vol. 109, No. 43, 2005

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Figure 2. (a) Definition of the angles R, β, and γ characterizing the orientation of various molecule-fixed vectors of interfacial waters and the polar angles ϑ and φ of the interface normal vector pointing to the vapor phase X in a local Cartesian frame fixed to the water molecule. (b) Definition of the angles γOMe, γOH, and γn characterizing the orientation of various molecule-fixed vectors of interfacial methanols and the polar angles ϑ and φ of the interface normal vector X in a local Cartesian frame fixed to the methanol molecule.

mole fractions of methanol in these three layers as well as in the bulk liquid part (defined to be the 10 Å wide layer located in the middle of the liquid phase) of the systems simulated are collected in Table 1. As is seen from these data, layer A and, at least partly, also layer B are located in the region of the adsorption peak of the methanol molecules, whereas layer C falls in the X range of the depletion layer, as the mole fraction of methanol is higher in layers A and B and lower in layer C than in the bulk part of the system. The composition of the bulk part is found to agree well with the overall composition of the system in every case. It is also clear from Table 1 that the vapor side of the interfacial layer (covered roughly by layer A) becomes nearly saturated with methanol molecules at relatively low bulk methanol concentrations. Thus, in the 20% methanol system (characterized by the bulk methanol mole percentage of about 17%), this layer already contains 70% methanol, and hence, the composition of this layer depends only rather weakly on the methanol concentration of the liquid phase above 20%. This finding is again in accordance both with the results of previous simulations23 and with the experimental results of Chen et al.32 3.2. Orientation of the Interfacial Water Molecules. 3.2.1. Orientational Profiles. To analyze the dependence of the orientational preferences of the water molecules on the distance from the interface, we have calculated the profile of three orientational parameters along the interface normal axis X. The profiles of these orientational parameters are defined as

ΦR(X) ) Fw(X)〈cos R〉(X)

(2)

Φβ(X) ) Fw(X)〈cos β - 0.5〉(X)

(3)

Φγ(X) ) Fw(X)〈cos γ - 0.5〉(X),

(4)

and

where R, β, and γ are the angles formed by the interface normal vector pointing to the vapor phase X with the water dipole vector, the molecular normal vector, and the vector joining the two H atoms of the water molecule (referred to here as the H-H vector), respectively, and the brackets 〈...〉 denote ensemble averaging. The definition of the angles R, β, and γ is illustrated in Figure 2a. It should be noted that the orientational parameters ΦR, Φβ, and Φγ are defined in such a way that their value becomes zero both when the density of the water molecules vanishes and in the case of uncorrelated orientation of the water molecules with the interface. The former property of these parameters simply comes from the fact that the orientational averages in eqs 2-4 are multiplied by the water molecular number density Fw, whereas the latter condition is fulfilled by

Figure 3. Profiles of the water orientational parameters ΦR (second panel), Φβ (third panel), and Φγ (bottom panel) along the interface normal axis X in systems of seven different compositions simulated. The water molecular number density profiles of the corresponding systems are also shown for reference (top panel). Solid curves, 0%; dotted lines, 5%; dash, 10%; dash-dot-dot, 20%; full circles, 30%; asterisks, 50%; open circles, 90% methanol system. For the definition of the shown orientational parameters, see the text. All profiles shown are averaged over the two interfaces present in the basic simulation box.

the fact that the range of possible values of the orientational parameter to be averaged (i.e., cos R, (cos β - 0.5) and (cos γ - 0.5), respectively) is symmetric to zero in each case.50-52 The orientational profiles obtained in seven different systems simulated are shown in Figure 3. The corresponding water molecular number density profiles are also shown for reference. As is seen, all three orientational profiles exhibit a single peak in the X range within which the water density drops from a bulklike value to zero, whereas all the orientational profiles are dropped to zero in the X range of the methanol depletion layer, where the water density is higher than in the bulk liquid phase. The sign of the peaks indicate that the dipole vector of the interfacial water molecules points to the liquid rather than to the vapor phase; the orientation of the molecular normal vector is closer to the parallel than to the perpendicular alignment relative to the interface normal vector X, whereas the H-H vector has an opposite orientational preference. It is also seen from Figure 3 that the Φγ(X) profile has two consecutive peaks in pure water, i.e., the main (negative) peak is followed by a smaller positive peak at the vapor side of the interface. However, this positive peak already disappears in the system containing 5% methanol and is also completely absent in the other methanol-containing systems. 3.2.2. Orientational Distribution of Molecule-Fixed Vectors. To get a deeper insight into the orientational preferences of the above three vectors fixed to the water molecules, we have calculated the cosine distribution of the angles R, β, and γ in the three separate interfacial layers defined in a previous


J. Phys. Chem. B, Vol. 109, No. 43, 2005 20497

Figure 4. Cosine distribution of the angles (a) R, (b) β, and (c) γ characterizing the orientation of various molecule-fixed vectors of the interfacial water molecules in the three separate interfacial layers of four different systems simulated. The definition of the angles R, β, and γ is illustrated in the inset of the top panels. Solid curves, 0%; dotted lines, 5%; squares, 25%; asterisks, 50% methanol system. For the definition of the different layers, see the text.

subsection. The resulting cosine distribution functions are shown in Figure 4 as obtained in four systems of different compositions. As is seen, in layer A of the pure water system, the dipole vector of the molecules prefers to stay nearly perpendicular to the interface normal axis X (i.e., parallel with the interface itself); the sharp negative peak of the ΦR(X) profile in this region is simply due to the fact that the molecular dipole vectors deviate from this preferred alignment more likely by pointing slightly to the liquid phase than in the opposite way. This finding is consistent with the results obtained at different water-apolar interfaces.19,50,51 However, this orientational preference of the water dipole vectors changes considerably in the presence of even a small amount of methanol. Thus, the main peak of P(cos R) shifts to smaller values with increasing methanol concentration: in the 5% methanol system, it is located at -0.3 (corresponding to the R value of 107°), whereas in the case of the 25% methanol system, the most probable value of cos R is already about -0.6, corresponding to R ≈ 125°. The dipole vectors of the water molecules located in layer B show similar, although considerably weaker, orientational preferences than in layer A, whereas in layer C, all orientational preferences are found to be already lost. The cosine distribution of the angle β has its peak at 1 (i.e., at β ) 0°) both in layers A and B of each of the systems studied, indicating that the plane of the interfacial water molecules prefers to lay parallel with the interface, independent from the methanol content of the system. However, similarly to P(cos R) the P(cos γ), distributions again show a marked difference between pure water and the systems containing methanol. Namely, in layer A, the P(cos γ) distribution, in accordance with the results obtained at various different waterapolar interfaces,19,50,51 peaks at 1 (i.e., at γ ) 0°) in the case of pure water, whereas in the presence of methanol in the system, this orientational preference is reversed: in layer A of these systems, the P(cos γ) distribution, although being rather flat, peaks at 0 rather than 1. In other words, in pure water, the H-H vector of the molecules at the vapor side of the interface prefers to stay perpendicular, whereas in water-methanol

mixtures, it prefers to be parallel with the plane of the interface. On the other hand, in layer B, the obtained P(cos γ) distribution has its peak at 0 and decreases monotonically in the entire cosine range between 0 and 1 in each of the systems studied, whereas in layer C, no orientational preference of the H-H vectors is observed. These findings indicate that the presence of methanol in the system considerably affects the orientational preferences of the water molecules located at the vapor side of the interface but leaves the orientation of the water molecules at the liquid side of the interface unaffected. 3.2.3. Orientation of the Entire Water Molecules. As we have demonstrated several times, the orientational preferences of the entire molecules relative to an interface can only be described unambiguously by the bivariate distribution of two independent orientational parameters.50-52 We have also shown that the angular polar coordinates ϑ and φ of the interface normal vector in a Cartesian frame fixed to the individual molecules are a suitable choice as orientational parameters for this purpose.50,51 In the present study, this local Cartesian frame is defined in such a way for the water molecules that its x, y, and z axes coincide with the normal vector, the H-H vector, and the dipole vector of the molecule, respectively. Therefore, the angle ϑ is equivalent with R, whereas φ is the vector formed by the molecular normal vector with the projection of the interface normal vector X to the plane perpendicular to the molecular dipole vector. Thus, in the case of ϑ ) 90°, φ becomes equivalent with β. The definition of the local Cartesian frame and that of the angles ϑ and φ is illustrated in Figure 2a. It should be noted that, while the angle ϑ is formed by two spatial vectors, φ is the angle of two vectors that are restricted to a certain plane by definition, and therefore, uncorrelated orientation of the water molecules with the interface results in uniform distributions of the variables cos ϑ and φ. The bivariate joint distributions of cos ϑ and φ are shown in Figure 5 as obtained in the three separate interfacial layers of six different systems simulated. The results obtained in pure water are consistent with our previous results observed at various different water-apolar interfaces,19,50,51 indicating that the water


Pa´rtay et al.

Figure 5. Orientational maps of the interfacial water molecules located at the interfacial layers C (first column), B (second column), and A (third column) of six different systems simulated. The maps corresponding to the 0%, 5%, 10%, 20%, 30%, and 50% methanol systems are shown in the respective rows from top to bottom. Lighter colors indicate higher probabilities. The peaks corresponding to the preferred orientations I and II in neat water are marked in the orientational map of layer A of this system.

molecules located closest to the vapor phase (i.e., in layer A) have two distinct orientational preferences. In the first of these two preferred orientations, reflected in the presence of a clear peak at cos ϑ ) 0 and φ ) 0° at the orientational map, the molecule lays parallel with the plane of the interface. This orientation is referred to as orientation I. In the other orientation preferred by the molecules of layer A, the plane of the water molecule is perpendicular to the interface; the dipole vector points flatly, whereas one of the O-H bonds points straight to the vapor phase. This orientation, corresponding to the peak at cos ϑ ) 0.5 and φ ) 90° is referred to here as orientation II. In layer B, similarly to other water-apolar interfaces,19,50,51 only

the peak corresponding to orientation I is present, whereas in layer C, the orientation of the water molecules is already uncorrelated with the interface. The orientational maps presented in Figure 5 clearly show, however, that the addition of even a small amount of methanol to the system leads to dramatic changes in the orientational preferences of the interfacial water molecules. Thus, the peak corresponding to orientation II already disappears in the 5% methanol system, whereas the peak of orientation I is shifted to somewhat smaller cos ϑ values and becomes broader along the φ axis of the map. This broadening of peak I, observed also in layer B, is related, at least partly, to the fact that with



Figure 6. (a) Arrangement of a hydrogen-bonded pair of water molecules, both of which are aligned in one of the orientations preferred at the vapor-liquid interface of neat water. The water molecule located closer to the vapor phase has orientation II; the other one has orientation I. (b) Arrangement of a hydrogen-bonded pair of a water and a methanol molecule, both of which are aligned in the orientation preferred at the liquid-vapor interface of water-methanol mixtures. The vector X is the interface normal, pointing toward the vapor phase.

increasing methanol concentration the number of water molecules present in layers A and B drops progressively, and hence, the statistical noise of the obtained bivariate distributions becomes, in particular in layer A, considerably larger. Nevertheless, it is clear that, in contrast with pure water, in the presence of methanol in the system the interfacial water molecules have only one orientational preference, which is rather similar to orientation I preferred in neat water and roughly corresponds to the cos ϑ and φ values of -0.5 and 0°, respectively. The orientations I and II preferred by the molecules at the liquidvapor interface of pure water as well as the orientation preferred by the water molecules in water-methanol mixtures are illustrated in Figure 6. 3.3. Orientation of the Interfacial Methanol Molecules. 3.3.1. Orientation of Molecule-Fixed Vectors. To characterize the interfacial orientation of the methanol molecules, we have defined, similarly to water, orientational parameters describing the alignment of various molecule-fixed vectors relative to the interface normal. Here, we have chosen three of such vectors, i.e., the vector pointing from the O atom to the methyl group (O-Me vector), the vector pointing from the O to the H atom (O-H vector), and the normal vector of the methanol molecule. The angles formed by the interface normal vector pointing to the vapor phase X with the O-Me, the O-H, and the molecular normal vectors are denoted by γOMe, γOH, and γn, respectively. The definition of these angles is shown in Figure 2b. To investigate the average orientation of these vectors relative to the interface along its normal axis X, we have calculated the profiles of the orientational parameters ΦOMe(X) and ΦOH(X), defined in analogy with the water orientational parameters as

ΦOMe(X) ) Fm(X)〈cos γOMe〉(X)

(5)

ΦOH(X) ) Fm(X)〈cos γOH〉(X).

(6)

and

The ΦOMe(X) and ΦOH(X) profiles obtained in seven of the systems simulated are shown in Figure 7, along with the methanol molecular number density profiles of the respective systems. As is seen, all the profiles have one sharp peak, located in the X range of the methanol adsorption layer. The sign of this peak is positive in the case of the O-Me vector and negative for the O-H vector, indicating that the interfacial methanol molecules tend to point outward (i.e., to the vapor phase) by

Figure 7. Profiles of the methanol orientational parameters ΦOMe (middle panel) and ΦOH (bottom panel) along the interface normal axis X in systems of seven different compositions simulated. The methanol molecular number density profiles of the corresponding systems are also shown for reference (top panel). Dotted lines, 5%; dash, 10%; dash-dot-dot, 20%; full circles, 30%; asterisks, 50%; open circles, 90%; short dash, 100% methanol system. For the definitions of the orientational parameters shown, see the text. All profiles shown are averaged over the two interfaces present in the basic simulation box.

their methyl group and inward by their H atom. Beyond this peak, the orientational profiles drop to zero, indicating that the orientation of at least these two molecule-fixed vectors chosen becomes uncorrelated with the interface beyond the methanol adsorption layer. The cosine distributions of the angles γOMe, γOH, and γn in the three separate interfacial layers, shown in Figure 8, are in accordance with the above findings. Thus, the P(cos γOMe) distributions are increasing monotonically both in layers A and B, indicating the preference of the interfacial methanol molecules for pointing straight away from the liquid phase by their methyl group. The fact that the preferred tilt angle of the methyl group relative to the interface normal axis is found to be 0° is in perfect accordance with the experimental results of Chen et al.32 On the other hand, the half-maximum width of the distributions, resulting in about 45° in layer A of the 5% methanol system and 60° in layer A of neat methanol, is considerably broader than what was found by Chen et al.,32 but it is in reasonable agreement with the results of some earlier SFG experiments.1-3 It is also evident that, although the strength of this orientational preference, at least in layer A, shows only a very weak dependence on the methanol mole fraction of the system, the distribution is slightly sharper in systems of lower methanol concentrations. (The composition dependence of the strength of the orientational preference is more evident in layer B; however, it can easily be due to the arbitrariness of the definition of the interfacial layers, i.e., to the fact that layer B might already contain an unknown number of molecules of uncorrelated orientation with the interface.) This finding is also in accordance with the results of previous computer simulation studies,23,30 as well as with some of the SFG measurements,2,29


Pa´rtay et al.

Figure 8. Cosine distribution of the angles (a) γOMe, (b) γOH, and (c) γn characterizing the orientation of various molecule-fixed vectors of the interfacial methanol molecules in the three separate interfacial layers of seven different systems simulated. The definition of the angles γOMe, γOH, and γn is illustrated in the inset of the top panels. Dotted lines, 5%; dash, 10%; dash-dot-dot, 20%; full circles, 30%; asterisks, 50%; open circles, 90%; short dash, 100% methanol system. For the definition of the different layers, see the text.

but conflicts with the results of the recent measurements of Chen et al.32 The orientational preference of the O-H vector, similar to that of the O-Me vector, does not show any change with the composition of the system neither in layer A nor in B. Thus, the P(cos γOH) distribution always peaks at about -0.4, corresponding to the γOH value of about 115°, indicating that in its preferred orientation the O-H vector of the methanol molecules prefers to decline by about 25° from the plane of the interface pointing to the liquid phase. The strength of this orientational preference depends negligibly on the composition of the system in the vapor side of the interface (i.e., in layer A). The obtained P(cos γn) distributions peak at 0 in layer A of the systems of low or medium methanol mole fractions, indicating that the plane of the methanol molecules located here prefers to align perpendicularly to the interface. However, this preference is rather weak and disappears almost completely in layer A of systems of methanol content above 50% as well as in layer B of all systems investigated. 3.3.2. Orientation of the Entire Methanol Molecules. In analyzing the orientational preferences of the entire methanol molecules relative to the interface, we have to define again the local Cartesian frame fixed to the individual methanol molecules, in which the polar angles ϑ and φ of the interface normal vector pointing to the vapor phase X is then determined. Here, we define this local frame in such a way that its x axis coincides with the vector pointing from the Me group to the O atom of the molecule (i.e., opposite to the O-Me vector defined in the previous subsection); the xy plane lays in the plane of the molecule, with the y coordinate of the H atom being negative, and the z axis is the molecular normal vector. Because of this definition, the angle ϑ, which is equivalent with γn, falls in the range 0-90° (and hence 0 e cos ϑ e 1), whereas the angle φ, formed by the projection of the interface normal vector pointing to the vapor phase X to the molecular plane with the vector pointing from the Me group to the O atom of the molecule can take any value between 0° and 360°. The definition of this local

frame and of the polar angles ϑ and φ is illustrated in Figure 2b. The bivariate P(cos ϑ, φ) distributions of the methanol molecules are plotted in Figure 9 as obtained in the three separate interfacial layers of six different systems simulated. As is seen, in layers A and B, the orientational maps exhibit a single clear peak at cos ϑ ) 0 and φ ) 180°. This peak becomes somewhat less sharp upon increasing the methanol mole fraction in the system and becomes considerably less sharp upon moving from layer A to B. In layer C, similarly to water, the orientation of the methanol molecules has also lost any correlation with the interface. The position of the peak in layers A and B indicates that in their preferred orientation the interfacial methanol molecules are aligned perpendicularly to the plane of the interface, pointing straight to the vapor phase by their methyl group. This orientation of the methanol molecule is illustrated in Figure 6. It is also seen from Figure 9 that the peak of the methanol P(cos ϑ, φ) orientational maps is rather sharp along the φ, whereas it is quite broad and elongated along the cos ϑ axis. This finding can be interpreted as follows: Although the plane of the methanol molecule prefers to align perpendicularly to the interface, this preference is not very strong; whereas the preference of the O-Me vector for pointing as straight away from the liquid phase as possible (i.e., declining by the least possible angle from the interface normal vector X), within the constraint imposed by the alignment of the molecular plane is a much stronger orientational preference. To demonstrate this, we have calculated the distribution of the angle φ (i.e., integrated the P(cos ϑ, φ) bivariate distributions for all possible values of cos ϑ) in the systems simulated. The obtained P(φ) distributions, shown in Figure 10, are indeed considerably sharper than the P(cos γOMe) distributions shown in Figure 8a. (Note that in the case of ϑ ) 90°, which is the preferred value of ϑ, the angle φ becomes equivalent to -γOMe.) Thus, the integration of the P(φ) and P(cos γOMe) distributions reveal that in layer A of the 5% methanol system 30% and 55% of the molecules are aligned in



Figure 9. Orientational maps of the interfacial methanol molecules located at interfacial layers C (first column), B (second column), and A (third column) of six different systems simulated. The maps corresponding to the 10%, 20%, 30%, 50%, 90%, and 100% methanol systems are shown in the respective rows from top to bottom. Lighter colors indicate higher probabilities.

such a way that the O-Me vector deviates less than 15° and 30°, respectively, from the projection of X to the molecular plane (i.e., |180°- φ| is smaller than 15° and 30°, respectively). On the other hand, only about 8% and 30% of the molecules correspond to a γOMe value below 15° and 30°, respectively. A similar trend is seen in the systems of higher methanol mole fractions: in layer A of the pure methanol system, about 22% and 40% of the molecules correspond to the value of |180° - φ|, whereas 5% and 20% to the values of γOMe smaller than 15° and 30°, respectively. 3.4. Relation Between the Orientational Preferences of the Water and Methanol Molecules. In understanding the relation between the preferential orientation of the interfacial methanol

molecules and the changes in the orientational preferences of the interfacial water molecules caused by the presence of methanol in the system, we have to consider the fact that the two orientations preferred by the interfacial molecules in pure water (i.e., orientations I and II) correspond to the alignment of a hydrogen-bonded water pair, in which the molecule of orientation II is closer to the vapor whereas that of orientation I is closer to the liquid phase.50 The alignment of such a hydrogen-bonded water pair is illustrated in Figure 6a. However, the O-H group of the methanol molecules in their preferred orientation is aligned in a very similar way to the hydrogen bonding O-H group of the water molecule of orientation II, and hence, these water molecules can be replaced by methanols


Figure 10. Distribution of the polar angle φ describing the relative orientation of the projection of the interface normal vector pointing to the vapor phase X to the plane of the methanol molecule and the molecule-fixed vector pointing from the methyl group to the O atom of the methanol molecule in layer A of seven different systems simulated. Dotted lines, 5%; dash, 10%; dash-dot-dot, 20%; full circles, 30%; asterisks, 50%; open circles, 90%; short dash, 100% methanol system.

in this hydrogen-bonding scheme, as demonstrated in Figure 6b. It should also be noted that the preferred orientation of the interfacial methanol molecules is a consequence of the hydrophobic nature of their methyl group, whereas the type II orientation of the interfacial water molecules is stabilized right by the hydrogen bond they can form with the other interfacial water molecules of orientation I. Therefore, the replacement of these type II waters by methanols in the hydrogen bonds should correspond to a decrease of the free energy of the interface. A similar effect has been observed at the interface of water with liquid 1-octanol as well as at the liquid-vapor interface of water containing adsorbed octanol molecules.55 Finally, the fact that this exchange of the outermost water molecules of orientation II to methanols is strong enough to result in the disappearance of the peak of orientation II at the P(cos ϑ, φ) orientational map already in the system containing only 5% methanol can be explained by the strong adsorption of the methanol molecules at the vapor side of the interface, i.e., by the fact that layer A of the 5% and 10% methanol systems already contain 40% and 58% methanol, respectively (see Table 1). 4. Summary and Conclusions In this paper, we have reported a series of Monte Carlo computer simulations of the vapor-liquid interface of watermethanol mixtures of different compositions, ranging from pure water to pure methanol. In accordance with recent experimental results,32 we have observed a double-layer structure of the interface: the outer interfacial layer is characterized by a strong adsorption of methanol molecules, whereas in the second layer, located at the liquid side of this adsorption layer, the density of methanol drops below the bulk liquid-phase value. In systems containing less than 20% methanol, the dominant feature of the interface is the adsorption of methanol at the outer layer. The excess hydration free energy of the methanol molecules relative to the bulk liquid phase is found to be about -9 kJ/mol here, in good agreement with the experimental value of -7.1 ( 0.4 kJ/mol,32 also considering the fact that the experimental value is averaged over all possible compositions of the system. Above the bulk methanol mole fraction value of about 0.2, this adsorption layer becomes nearly saturated with

Pa´rtay et al. methanol molecules (a finding that is also in clear agreement with experimental observations32), and hence, the magnitude of the excess hydration free energy of the methanols in this layer drops rapidly to zero with a further increase of the methanol content of the system. On the other hand, in systems containing 25-50% methanol, the interfacial structure is dominated by the presence of the methanol depletion layer. The excess hydration free energy of the methanol molecules in this layer is found to be about 2.5-5 kJ/mol in the methanol mole fraction range between 0.25 and 0.5 and about 1-1.5 kJ/mol below and above this composition range. These results are again in good agreement with the experimental figure of 2.1 ( 1.7 kJ/mol, obtained again as an average over all possible compositions of the system.32 In analyzing the orientation of the molecules, we have found that the influence of the interface on the molecular orientation vanishes rapidly, within a few layers of the interfacial molecules, and it is already absent among the molecules of the methanol depletion layer. The interfacial methanol molecules have a single orientational preference, in which their plane is aligned perpendicular to the interface and their methyl group points straight to the vapor phase. The preference of the molecular plane for this perpendicular alignment is found to be rather weak. As a consequence, the distribution of the tilt angle of the methyl group relative to the interface normal is also found to be rather broad, certainly considerably broader than what has been observed by Chen et al. in their recent SFG measurement using the PNA method,32 but consistent with the conclusions drawn in several earlier SFG experiments.1-3 However, we have also observed a much stronger orientational preference of the interfacial methanol molecules, namely that within the constraint imposed by the orientation of the molecular plane the methyl group prefers to point as straight to the vapor phase as possible. In analyzing the orientation of the interfacial water molecules, we have found that in the presence of methanol one of their orientations preferred in the interfacial water molecules in the neat system disappears, as the water molecules of this orientation can be replaced by methanols aligned in their preferred orientation. Similar behavior has been observed at the liquidvapor interface of water in the presence of adsorbed octanol molecules.55 This effect is found to be rather strong even at low methanol mole fractions because of the strong adsorption of the methanol molecules at the outer layer of the interface. Acknowledgment. This project is supported by the Hungarian OTKA Foundation under project no. T049673 and by the Hungarian-Chinese Intergovernmental Science and Technology Program under project no. CHN-26/04. We are grateful to Dr. Hongfei Wang (Institute of Chemistry, Chinese Academy of Sciences, Beijing, China) for providing the manuscript of ref 32 prior to publication. P. J. is a Be´ke´sy Gyo¨rgy fellow of the Hungarian Ministry of Education, which is gratefully acknowledged. References and Notes (1) Superfine, R.; Huang, J. Y.; Shen, Y. R. Phys. ReV. Lett. 1991, 66, 1066. (2) Wolfrum, K.; Graener, H.; Laubereau, A. Chem. Phys. Lett. 1993, 213, 41. (3) Stanners, C. D.; Du, Q.; Chin, R. P.; Cremer, P.; Somorjai, G. A.; Shen, Y. R. Chem. Phys. Lett. 1995, 232, 407. (4) Taylor, R. S.; Dang, L. X.; Garrett, B. C. J. Phys. Chem. 1996, 100, 11720. (5) Gragson, D. E.; Richmond, G. L. J. Phys. Chem. B 1998, 102, 3847. (6) Wilson, M. A.; Pohorille, A.; Pratt, L. J. Chem. Phys. 1988, 88, 3281.

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Structure of the Liquidâ Vapor Interface of Waterâ Methanol Mixtures

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